books.google.com - The aim of this book is to explain modern homotopy theory in a manner accessible to graduate students yet structured so that experts can skip over numerous linear developments to quickly reach the topics of their interest. Homotopy theory arises from choosing a class of maps, called weak equivalences,...http://books.google.com/books/about/Model_Categories_and_Their_Localizations.html?id=LH8CoWJfHloC&utm_source=gb-gplus-shareModel Categories and Their Localizations

Model Categories and Their Localizations

The aim of this book is to explain modern homotopy theory in a manner accessible to graduate students yet structured so that experts can skip over numerous linear developments to quickly reach the topics of their interest. Homotopy theory arises from choosing a class of maps, called weak equivalences, and then passing to the homotopy category by localizing with respect to the weak equivalences - by creating a new category in which the weak equivalences are isomorphisms.